This invention relates to a two reactor process for the continuous manufacture of dialkyl disulfides and polysulfides from alkenes, hydrogen sulfide (H.sub.2 S) and sulfur in the presence of solid particulate catalysts. More particularly, it relates to a process for the continuous manufacture of dialkyl disulfides and/or dialkyl polysulfides by reacting an alkene with H.sub.2 S over a solid, particulate catalyst in a first reaction zone, and then passing the first reactor effluent into a second reaction zone, where it is reacted with elemental sulfur in the presence of a solid, particulate catalyst.